Results 71 to 80 of about 8,177 (202)
Bifurcation diagrams for singularly perturbed system: the multi-dimensional case.
Electronic Journal of Qualitative Theory of Differential Equations, 2013 We consider a singularly perturbed system where the fast dynamics of the unperturbed problem exhibits a trajectory homoclinic to a critical point. We assume that the slow time system admits a unique critical point, which undergoes a bifurcation as a ...
Matteo Franca
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Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
, 2016 We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu.
Ovsyannikov, I. I., Turaev, D. V.
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Bifurcation Analysis of Nonlinear Oscillations in the Electrical Activity of Pancreatic β‐Cells
Proceedings in Applied Mathematics and Mechanics, Volume 25, Issue 4, December 2025.ABSTRACT Cell biological systems are characterized by complex relationships and nonlinear processes. The modeling of these processes improves the understanding, and represents a significant enrichment of the experimental investigation. An example of such a system is the regulation of blood glucose concentration by pancreatic β$\beta$‐cells through the ...
Paula Clasen +2 more
wiley +1 more source
Simple-Zero and Double-Zero Singularities of a Kaldor-Kalecki Model of Business Cycles with Delay
Discrete Dynamics in Nature and Society, 2009 We study the Kaldor-Kalecki model of business cycles with delay in both the gross product and the capital stock. Simple-zero and double-zero singularities are investigated when bifurcation parameters change near certain critical values.
Xiaoqin P. Wu
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Spatial Effects of Phase Dynamics on Oscillators Close to Bifurcation
Mathematics, 2023 The phase reduction approach has manifested its efficacy in investigating synchronization behaviors in limit-cycle oscillators. However, spatial distributions of the phase value on the limit cycle may lead to illusions of synchronizations for oscillators
Yihan Wang, Jinjie Zhu
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Delay-induced multistability near a global bifurcation
, 2007 We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node.
E. SCHÖLL +5 more
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Chaos and Control in Coronary Artery System
Discrete Dynamics in Nature and Society, 2012 Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method.
Yanxiang Shi
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Resonance bifurcation from homoclinic cycles
Journal of Differential Equations, 2009 Consider a dynamical system \(x' = f(x)\) in \(\mathbb{R}^n\), and a group \(G\) (in this case a finite group) acting in \(\mathbb{R}^n\) through a linear representation. The dynamnical system is \(G\)-symmetric if \(f (g x) = g f(x)\) for all \(x\) and all \(g \in G\).
Driesse, R., Homburg, A.J.
openaire +4 more sources
Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
wiley +1 more source
Multistable Solitons in the Cubic-Quintic Discrete Nonlinear Schr\"odinger Equation
, 2005 We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities.
Alfimov +53 more
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